Positron Emission tomography (PET) is a major molecular imaging tool in oncology, with applications ranging from diagnosis and staging to patient management. Despite the broad use of PET in the clinical environment, there is no quantitative PET imaging method available for routine clinical practice. The currently used static scan can provide a semi-quantitative measurement, standardized uptake value (SUV), for a whole body scan. However, it completely ignores the dynamic nature of radiopharmaceutical kinetics. The popular semi-quantitative dual time point method can approximate the kinetic differences at two time points by comparing activities but usually requires an extended waiting time for the second scan. The multiple time point method can calculate the net influx rate but still requires long scan duration and makes a whole body scan infeasible. The challenge of a quantitative whole body dynamic PET scan lies in how to estimate the quantitative functional values, such as net flux rate, using data from a short acquisition period, and how to accelerate the computation to make it practical in a clinical setting. We address this challenge by developing and optimizing a novel data analysis method and implementing it using a high performance computing tool. We take advantage of the linearity of Patlak graphic analysis to model the tracer activity in each voxel as a linear combination of the blood input function and its integral, weighted by the Patlak parameters including net influx rate. In addition, we derive a simplified model of the blood input function, based on the same assumptions used to derive Patlak parameters from the kinetic compartment model. We then estimate the Patlak parameters and the parameters in the blood input function in a penalized maximum likelihood estimation framework using the list mode data and its associated inhomogeneous Poisson statistical model. We also theoretically analyze the performance of our Patlak estimator in terms of noise, resolution and signal-to-noise ratio (SNR), and use the results to guide us in optimizing the scan duration and any movement of imaging bed to achieve the best SNR. The advanced estimation algorithm, along with an accurate imaging system model, can robustly compute the net influx rate using the list mode data in a short acquisition without a measured blood input function, and make whole body dynamic scans practical. Our algorithms will be implemented on an Nvidia Tesla GPU (graphics processing unit) based workstation, a new computing tool that provides computational power previously available only on a mini super computer. We will further accelerate our algorithms using a combination of efficient representation of the list mode data and the system matrix. We will evaluate the performance of the proposed method and compare it with SUV, the dual time point method, and the traditional Patlak method, using simulated and clinical data. We will use a range of performance metrics, including region of interest (ROI) bias, ROI variance, lesion detectability, and computer and human observers. This project will eventually provide a quantitative dynamic whole body PET imaging protocol that can potentially improve the sensitivity and specificity of PET imaging in oncology.